This paper presents an estimation method for the random effect parameters and the variance components in linear mixed models. These models may be orthogonal or nonorthogonal. In particular, least squares estimators and the corresponding confidence regions, based on the estimation of quantiles, are considered. As to the random effects parameters, it is only assumed that they have null mean vectors and distributions with known dispersion parameters and second order moments. So, it is not necessary that they are normally distributed. A numerical example considering the normal and the gamma distributions is included, where a comparison with the analysis of variance and a Bayesian estimation based method is provided.
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